1. Averages Generally, this involves adding the values present and then dividing by the number of values. For example, you may be asked to calculate the average height of a plant from a set of results: Plant
Plant height (cm) 10 14 9
A B C
Average = (10 + 14 + 9) / 3 = 11 cm
You may also be asked to calculate an average increase or decrease over a set period of time. You must first calculate the increase or decrease and then divide by the length of time.
For example, "Calculate the average increase in glucose concentration per minute."
Time (minutes) 0 5 10
Glucose concentration (mg/ml) 12 27 40
Change in 10 minutes = 12 increasing to 40, = 28 Change per minute
so 40-12
= 28 ÷ 10 = 2.8 mg/ml
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2. Ratios Ratios involves comparing two (or sometimes three) numbers and simplifying them into their smallest values. It is always kept to whole numbers. Firstly write them out next to each other with a colon ( : ) separating them. The divide them both separately by the largest number they both divide into. For example, "Express in a whole number the ratio of starch to maltose in a barley grain.”
Starch Maltose 70 35
70 : 35 Divide both by 35, so
70÷35 : 35÷35 2:1
For example, “Express the number of pupils of each blood group in a class as a whole number ratio.” AB 9
A 12
9 : 12 Divide all by 3, so
B 6
: 6
9÷3 : 12÷3 : 6÷3 3
:
4
:
2
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3. Percentages Percentages compare an amount of something to its total. Divide the amount by the total and then times by 100. For example, 2 out of 50 people are likely to develop high blood pressure in Scotland. What percentage is this? = (2 ÷ 50) x 100 = 4%
4. Percentage changes Percentage changes compare how much something has changed. It might be an increase or a decrease, but you work it out the same. Calculate the change that has happened, divide it by the value at the start and then times by 100. For example: "Blood pressure decreases from 15 to 3 units as it moves into the veins. Calculate the percentage decrease in blood pressure." Percentage decrease = change ÷ start value x 100 = (15 – 3) ÷ 15 x 100 = 12 ÷ 15 x 100 = 80%
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5. Numbers from percentages Numbers from percentages works out the actual number from a percentage given. Calculate this by dividing the percentage by 100, then times by the value you are working out.
For example, 95% of the class of 20 pupils voted in favour of using stem cells in Scotland on the NHS. What number is this? = (95 ÷ 100) x 20 = 19 pupils
Questions to try!
Averages 1. I added up the heights of boys in a 4th year class and found they were 156cm, 148cm, and 2 at 152cm. What was the average height?
_______ cm 2. Looking at seed fertilisation with 20 plants in 3 experiments: 5 were fertilised in the first, 7 in the second and 3 in the third. What was the average number of plants fertilised?
_________ 3. The number of nuclear explosions in Canada was found to be 12 last year, 15 in Britain and 3 in France. What was the average number of explosions?
__________
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Ratios 4. What is the ratio between 15 diabetic, 10 anaemic and 25 leukaemia sufferers?
__________ Diabetes
:
_____________ Anaemia
: ____________ Leukaemia
5. The biology department spends £160 a week, the chemistry department spends £120 a week and physics department spends £160 a week. Write these as a ratio.
_________ biology
: ________ : __________ chemistry physics
6. After exercising for 4 minutes, Al’s breathing rate is 16bpm but Louise’s is 24 bpm. Write their breathing rates as a ratio.
_______ : _______ Al : Louise
Percentages
7. 3 out of 30 people in the UK have diabetes. What percentage is this?
_____ % 8. 20 out of 80 people in the UK suffer high blood pressure. What percentage is this?
_____ % 6
9. A class sowed 25 mustard seeds. From the table below, what percentage of these seeds germinated? Number of seeds sown 5
Number of seeds germinated 25
_____ %
Percentage changes
10. The average lifespan of a Scottish man has increased from 70-75 years. What percentage increase is this?
______ % 11. Cress seeds increased in length on average from 10mm to 25mm with the use of fertiliser. What percentage increase is this?
_____ %
12. A class experiment measured the volume of dough before and after adding yeast. It started off at 12ml and ended up at 24 ml. What percentage increase is this?
_____ %
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Numbers from percentages
13. 25% of the class of 20 are over 150cm in height. What number is this?
________
14. I looked at 40 girls in 5th year and found that 50% of them had brown hair and 10% had blonde hair. How many girls had a) brown hair and b) blonde hair?
________ brown ________ blonde 15. 20% of 200 people surveyed in Fife have had ‘flu. What number is this?
________
16. KHS had £150 to spend on science jotters. It only spent 30% how much is this?
